Problem: The sum of two numbers is $23$, and their difference is $3$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 23}$ ${x-y = 3}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 26 $ $ x = \dfrac{26}{2} $ ${x = 13}$ Now that you know ${x = 13}$ , plug it back into $ {x+y = 23}$ to find $y$ ${(13)}{ + y = 23}$ ${y = 10}$ You can also plug ${x = 13}$ into $ {x-y = 3}$ and get the same answer for $y$ ${(13)}{ - y = 3}$ ${y = 10}$ Therefore, the larger number is $13$, and the smaller number is $10$.